Question: Solve for $x$ : $ 5|x + 8| + 10 = 4|x + 8| + 3 $
Subtract $ {4|x + 8|} $ from both sides: $ \begin{eqnarray} 5|x + 8| + 10 &=& 4|x + 8| + 3 \\ \\ { - 4|x + 8|} && { - 4|x + 8|} \\ \\ 1|x + 8| + 10 &=& 3 \end{eqnarray} $ Subtract ${10}$ from both sides: $ \begin{eqnarray} 1|x + 8| + 10 &=& 3 \\ \\ { - 10} &=& { - 10} \\ \\ 1|x + 8| &=& -7 \end{eqnarray} $ Simplify: $ |x + 8| = -7$ The absolute value cannot be negative. Therefore, there is no solution.